Question

In a daily meeting, the Chief Financial Officer (CFO) gave Ari the following table of market rates:

Spot exchange rate: Yen 106/$

U.S. dollar interest rate per annum 10%

Japanese Yen interest rate per annum 6%

and told Ari that the company’s financial analyst expected the Japanese Yen to depreciate against the U.S. dolla rby 3.46%in 90 days.Assume there are 360 days in a year, and all interest rates are simple interest rates.If the financial analyst’s prediction about the US dollar and Japanese Yen turned out to be true:

1) What would the spot exchange rate (Yen/$) be in 90 days?

2) Would Ari make a profit by borrowing 1 million US dollar and investing in the money markets? If yes, how much profit would Ari realise in 90 days? If no, explain why.

Answer 1

1)

Spot Exchange Rate in 90 Days

= Current Spot Rate * (1 + Japanese Yen Interest Rate for 90 Days) / (1 + U.S. Dollar Interest Rate for 90Days)

= Yen 106 * (1 + 6%*90/360) / (1 + 10%*90/360)

= Yen 106 * (1 + 1.5%) / (1 + 2.5%)

= Yen 106 * (1.015) / (1.025)

= Yen 104.9658

2)

Actual Price of Japanese Yen in 90 Days is depreciated by 3.46% against $.

That means price of Yen will be more.

Actual Price of Japanese Yen in 90 Days

= Yen 106 + 3.46%

= Yen 109.6676

Actual Price (Yen 109.6676) > Thoretical Price (Yen 104.9658)

Therefore, arbitrage profit will be made if money borrowed in Yen.

But Ari borrows in $, therefore he will realise a loss as follows.

1) Borrow $1,000,000 @ 10% and convert in into Yen @ Yen 106/$

2) We will Receive Yen 106,000,000 ($1,000,000 * Yen 106)

3) Invest Yen 106,000,000 @ 6%

4) After 90 Days investment have value of Yen 107,590,000 (Yen 106,000,000*(1+6%*90/360))

5) Convert Yen 107,590,000 @ 90 Days Spot Rate i.e. Yen 109.6676 / $

6) We will receive $981,055.48 (Yen 107,590,000 / Yen 109.6676)

7) After 90 Days Borrowed Amount will be $1,025,000 ($1,000,000*(1+10%*90/360))

8) Arbitrage Loss will be $43,944.52($1,025,000 - $981,055.48)